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1. Consider heat diffusion problem in a finite rod with one insulated endpoint and another one kept at fixed temparature: ut@, t) ucc(c, t) 0, 0 < c < --, t > 0, 0) = 1 + cos(3c), 2 a) Write down the diffusion problem solved by the function v@, t) b) Solve the diffusion problem for v using the method of separation of variables. c) Find the solution u aof the original problem.